Thank you for taking the time to write a thoughtful reply.
Here is where I'm coming from:
No one expects a child to read and write before they know how to have a conversation.
Yet, as a student of calculus in high school, I was constantly "solving" problems completely outside of my imagination, which I liken to teaching a child to read and write, but this child does not know language and cannot hold a conversation.
If Feynman's advice were taken, mathematics education could only improve. Perhaps, my math education was not abstract enough (when I seem to be calling for something more concrete).
My wish is that, while solving those calculus equations, I would be able to "imagine" the problem, imagine the solution, imagine how the solution might change should the problem change... to have a sort of working mathematical... "vocabulary." Perhaps the words "imagine" and "vocabulary" are out of place here. Instead of all that, I felt I was just memorizing and manipulating symbols without meaning and without comprehension. I was literally just drawing pictures. Maybe that's all math is, a very abstract series of internally consistent manipulations. Maybe I just need more practice applying it in a wider variety of contexts.
But my hunch is that:
1. I should be able to know a lot of different problems and how to solve them, and only once that process has happened would I
2. later use symbolic notation to explain things I *already* know internally.
3. Finally, I would be able to use the symbolic notation to help me build new understandings.